arXiv subjects

Takahiko Matsubara

Publications and source records attributed to Takahiko Matsubara.

At least 91 records · Page 5Linked to original sources

arXiv2000

The Gravitational Lensing in Redshift-space Correlation Functions of Galaxies and Quasars

The gravitational lensing, as well as the velocity field and the cosmological light-cone warp, changes the observed correlation function of high-redshift objects. We present an analytical expression of 3D correlation function, simultaneously including those three effects. When two objects are separated over several hundreds Mpc along a line of sight, the observed correlation function is dominated by the effect of gravitational lensing rather than the intrinsic clustering. For a canonical lambda-CDM model, the lensing signals in the galaxy-galaxy and galaxy-QSO correlations are beyond noise levels in large-scale redshift surveys like the Sloan Digital Sky Survey.

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arXiv2000

Cosmological Parameters from the Eigenmode Analysis of the Las Campanas Redshift Survey

We present the first results of the Karhunen-Loève (KL) eigenmodes applied to real data of the Las Campanas Redshift Survey (LCRS) to simultaneously measure the values of the redshift-distortion parameter, $β= Ω_0^{0.6}/b$, the linearly extrapolated normalization, $σ_8^{\rm L}$, and the CDM shape parameter, $Γ= Ω_0 h$. The results of our numerical likelihood analysis indicate a low value of $β= 0.30 \pm 0.39$, a shape parameter $Γ= 0.16 \pm 0.10$, and a linearly extrapolated normalization $σ_8^{\rm L} = 0.79 \pm 0.08$, which are consistent with a low density universe, $Ω_0 \simlt 0.5$.

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arXiv2000

The Correlation Function in Redshift Space: General Formula with Wide-angle Effects and Cosmological Distortions

A general formula for the correlation function in redshift space is derived in linear theory. The formula simultaneously includes wide-angle effects and cosmological distortions. The formula is applicable to any pair with arbitrary angle $θ$ between lines of sight, and arbitrary redshifts, $z_1$, $z_2$, which are not necessarily small. The effects of the spatial curvature both on geometry and on fluctuation spectrum are properly taken into account, and thus our formula holds in a Friedman-Lema\^ıtre universe with arbitrary cosmological parameters $Ω_0$ and $λ_0$. We illustrate the pattern of the resulting correlation function with several models, and also show that validity region of the conventional distant observer approximation is $θ\le 10^\circ$.

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arXiv1999

Stochasticity of Bias and Nonlocality of Galaxy Formation: Linear Scales

If one wants to represent the galaxy number density at some point in terms of only the mass density at the same point, there appears the stochasticity in such a relation, which is referred to as ``stochastic bias''. The stochasticity is there because the galaxy number density is not merely a local function of a mass density field, but it is a nonlocal functional, instead. Thus, the phenomenological stochasticity of the bias should be accounted for by nonlocal features of galaxy formation processes. Based on mathematical arguments, we show that there are simple relations between biasing and nonlocality on linear scales of density fluctuations, and that the stochasticity in Fourier space does not exist on linear scales under a certain condition, even if the galaxy formation itself is a complex nonlinear and nonlocal precess. The stochasticity in real space, however, arise from the scale-dependence of bias parameter, $b$. As examples, we derive the stochastic bias parameters of simple nonlocal models of galaxy formation, i.e., the local Lagrangian bias models, the cooperative model, and the peak model. We show that the stochasticity in real space is also weak, except on the scales of nonlocality of the galaxy formation. Therefore, we do not have to worry too much about the stochasticity on linear scales, especially in Fourier space, even if we do not know the details of galaxy formation process.

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arXiv1999

Deciphering cosmological information from redshift surveys of high-z objects - the cosmological light-cone effect and redshift-space distortion -

The three-dimensional distribution of astronomical objects observed in redshift space significantly differs from the true distribution since the distance to each object cannot be determined by its redshift $z$ only; for $z \ll 1$ the peculiar velocity field contaminates the true recession velocity of the Hubble flow, while the true distance for objects at $z < 1$ sensitively depends on the (unknown and thus assumed) cosmological parameters. This hampers the effort to understand the true distribution of large-scale structure of the universe. In addition, all cosmological observations are carried out on a light-cone, the null hypersurface of an observer at $z=0$. This implies that their intrinsic properties and clustering statistics should change even within the survey volume. Therefore a proper comparison taking account of the light-cone effect is important to extract any cosmological information from redshift catalogues, especially for $z < 1$. We present recent theoretical development on the two effects -- the cosmological light-cone effect and the cosmological redshift-space distortion -- which should play key roles in observational cosmology in the 21st century.

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arXiv1997

Redshift Space Distortions of the Correlation Function in Wide Angle Galaxy Surveys

Using a novel two-dimensional coordinate system, we have derived a particularly simple way to express the redshift distortions in galaxy redshift surveys with arbitrary geometry in closed form. This method provides an almost ideal way to measure the value of $β=Ω_0^{0.6}/b$ in wide area surveys, since all pairs in the survey can be used for the analysis. In the limit of small angles, this result straightforwardly reduces to the plane-parallel approximation. This expansion can also be used together with more sophisticated methods such as for the calculation of Karhunen-Loeve eigenvectors in redshift space for an arbitrary survey geometry. Therefore, these results should provide for more precise methods in which to measure the large scale power spectrum and the value of $β$ simultaneously.

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arXiv1997

Light-cone effect on higher-order clustering in redshift surveys

We have evaluated a systematic effect on counts-in-cells analysis of deep, wide-field galaxy catalogues induced by the evolution of clustering within the survey volume. A multiplicative correction factor is explicitly presented, which can be applied after the higher order correlation functions have been extracted in the usual way, without taking into account the evolution. The general theory of this effect combined with the ansatz describing the non-linear evolution of clustering in simulations enables us to estimate the magnitude of the correction factor in different cosmologies. In a series of numerical calculations assuming an array of cold dark matter models, it is found that, as long as galaxies are unbiased tracers of underlying density field, the effect is relatively small ($ \simeq 10%$) for the shallow surveys ($z <0.2$), while it becomes significant (order of unity) in deep surveys ($z \sim1$). Depending on the scales of interest, the required correction is comparable to or smaller than the expected errors of on-going wide-field galaxy surveys such as the SDSS and 2dF. Therefore at present, the effect has to be taken into account for high precision measurements at very small scales only, while in future deep surveys it amounts to a significant correction.

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arXiv1997

Cosmological redshift distortion: deceleration, bias and density parameters from future redshift surveys of galaxies

The observed two-point correlation functions of galaxies in redshift space become anisotropic due to the geometry of the universe as well as due to the presence of the peculiar velocity field. On the basis of linear perturbation theory, we expand the induced anisotropies of the correlation functions with respect to the redshift $z$, and obtain analytic formulae to infer the deceleration parameter $q_0$, the density parameter $Ω_0$ and the derivative of the bias parameter $d\ln b/dz$ at $z=0$ in terms of the observable statistical quantities. The present method does not require any assumption of the shape and amplitude of the underlying fluctuation spectrum, and thus can be applied to future redshift surveys of galaxies including the Sloan Digital Sky Survey. We also evaluate quantitatively the systematic error in estimating the value of $β_0 \equiv Ω_0^{0.6}/b$ from a galaxy redshift survey on the basis of a conventional estimator for $β_0$ which neglects both the geometrical distortion effect and the time evolution of the parameter $β(z)$. If the magnitude limit of the survey is as faint as 18.5 (in B-band) as in the case of the Sloan Digital Sky Survey, the systematic error ranges between -20% and 10% depending on the cosmological parameters. Although such systematic errors are smaller than the statistical errors in the current surveys, they will dominate the expected statistical error for future surveys.

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arXiv1997

Beyond Zel'dovich-Type Approximations in Gravitational Instability Theory --- Padé Prescription in Spheroidal Collapse ---

Among several analytic approximations for the growth of density fluctuations in the expanding Universe, Zel'dovich approximation in Lagrangian coordinate scheme is known to be unusually accurate even in mildly non-linear regime. This approximation is very similar to the Padé approximation in appearance. We first establish, however, that these two are actually different and independent approximations with each other by using a model of spheroidal mass collapse. Then we propose Padé-prescribed Zel'dovich-type approximations and demonstrate, within this model, that they are much accurate than any other known nonlinear approximations.

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arXiv1997

Accuracy of Nonlinear Approximations in Spheroidal Collapse --- Why are Zel'dovich-type approximations so good? ---

Among various analytic approximations for the growth of density fluctuations in the expanding Universe, Zel'dovich approximation and its extensions in Lagrangian scheme are known to be accurate even in mildly non-linear regime. The aim of this paper is to investigate the reason why these Zel'dovich-type approximations work accurately beyond the linear regime from the following two points of view: (1) Dimensionality of the system and (2) the Lagrangian scheme on which the Zel'dovich approximation is grounded. In order to examine the dimensionality, we introduce a model with spheroidal mass distribution. In order to examine the Lagrangian scheme, we introduce the Padé approximation in Eulerian scheme. We clarify which of these aspects supports the unusual accuracy of the Zel'dovich-type approximations. We also give an implication for more accurate approximation method beyond the Zel'dovich-type approximations.

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arXiv1996

Nonlinear Evolution of the Genus Statistics with Zel'dovich Approximation

Evolution of genus density is calculated from Gaussian initial conditions using Zel'dovich approximation. A new approach is introduced which formulates the desired quantity in a rotationally invariant manner. It is shown that normalized genus density does not depend on the initial spectral shape but is a function of the fluctuation amplitude only.

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arXiv1996

Cosmological Redshift-Space Distortion II: distance in an inhomogeneous universe and evolution of bias

We discuss the two potentially important effects which should be taken into account in the analysis of the cosmological redshift-space distortion especially at high redshifts; the effect of inhomogeneities in the light propagation and the evolution of bias. Although such inhomogeneities affect significantly the degree of the cosmological redshift distortion, one can determine the density parameter $Ω_0$ from the distortion pattern at $z=0$, and the cosmological constant $λ_0$ from that at $z = (1\sim 2)$. In particular we show that in low-density ($Ω_0\ll 1$) universes one can determine the value of $λ_0$ and even the evolution of the bias parameter almost insensitively to the degree of the clumpiness of the matter distribution in the universe.

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arXiv1996

Cosmological Redshift Distortion of Correlation Functions as a Probe of the Density Parameter and the Cosmological Constant

We propose cosmological redshift-space distortion of correlation functions of galaxies and quasars as a probe of both the density parameter $Ω_0$ and the cosmological constant $λ_0$. In particular, we show that redshift-space distortion of quasar correlation functions at $z\sim2$ can in principle set a constraint on the value of $λ_0$. This is in contrast to the popular analysis of galaxy correlation functions in redshift space which basically determines $Ω_0^{0.6}/b$, where $b$ is the bias parameter, but is insensitive to $λ_0$. For specific applications, we present redshift-space distortion of correlation functions both in cold dark matter models and in power-law correlation function models, and discuss the extent to which one can discriminate between the different $λ_0$ models.

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arXiv1995

On Second-order Perturbation Theories of Gravitational Instability in Friedmann-Lemaitre Models

The Eulerian and Lagrangian second-order perturbation theories are solved explicitly in closed forms in $Ω\neq 1$ and $Λ\neq 0$ {}Friedmann-Lema\^ıtre models. I explicitly write the second-order theories in terms of closed one-dimensional integrals. In cosmologically interested cases ($Λ= 0$ or $Ω+ λ= 1$), they reduce to elementary functions or hypergeometric functions. For arbitrary $Ω$ and $Λ$, I present accurate fitting formula which are sufficient in practice for the observational cosmology. It is reconfirmed for generic $Ω$ and $Λ$ of interest that second-order effect only weakly depends on these parameters.

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arXiv1995

Nonlinear Evolution of Genus in Primordial Random-Gaussian Density Field

The genus statistics is studied using large $N$-body simulations for several cosmological models. We consider the effects of nonlinear gravitational evolution, smoothing the particle data in fully nonlinear regime, and the redshift-space distortion on the genus curve. Detailed comparison between the theoretical prediction in weakly nonlinear theory and the appropriate simulation results shows that the analytic formula describes the behavior of genus in weakly nonlinear regime fairly accurately. We also find that the redshift-space distortion on genus statistics is small in linear and weakly nonlinear regimes. We conclude that if weakly nonlinear theory and direct numerical simulations are combined, the normalized genus curve $G(ν)/G(0)$ is a powerful tool to directly check the random-Gaussian paradigm of the origin of the large-scale structure in the universe.

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arXiv1995

Genus Statistics of the Large-Scale Structure with Non-Gaussian Density Fields

As a statistical measure to quantify the topological structure of the large-scale structure in the universe, the genus number is calculated for a number of non-Gaussian distributions in which the density field is characterized by a nontrivial function of some Gaussian-distributed random numbers. As a specific example, the formulae for the lognormal and the chi-square distributions are derived and compared with the results of $N$-body simulations together with the previously known formulae for the Gaussian distribution and second-order perturbation theory. It is shown that the lognormal formula fits most of the simulation data the best.

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arXiv1995

Weakly Nonlinear Evolution of Topology of Large-scale Structure

The gravitational evolution of the genus and other statistics of isodensity contours of the density field is derived analytically in a weakly nonlinear regime using second-order perturbation theory. The effect of final smoothing in perturbation theory on the statistics of isodensity contours is also evaluated. The resulting analytic expression for the genus is compared with $N$-body numerical simulations and exhibits a good agreement.

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arXiv1995

Statistics of Isodensity Contours in Redshift Space

The peculiar velocities of galaxies distort the clustering pattern anisotropically in redshift space. This effect on the statistics of isodensity contours is examined by linear theory. The statistics considered in this paper are the three- and two-dimensional genus of isodensity contours, the area of isodensity contours, the length of isodensity contours in the 2-dimensional slice and the level crossing statistics on the line. We find that all these statistics in redshift space as functions of density threshold of contours have the same shape as in real space. The redshift space distortion affects only amplitudes of these statistics. The three-dimensional genus and the area hardly suffer from the redshift space distortion for $0 \leq Ωb^{-5/3} \leq 1$, where $b$ is a linear bias parameter. The other statistics are defined in one- or two-dimensional slices of the sample volume and depend on the direction of these slices relative to the line of sight. This dependence on direction of these statistics provides a way to determine the density parameter of the universe.

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